Genetic Improvement of Railway Timetables

We consider how to improve railway timetables. As case we take the Rompnet of the dutch railways, a highly constrained problem, containing both hard and soft constraints. We show how to cast the constraints into the format of the Genocop system. Every train should run every hour at the same time and hence the constraints should be interpreted modulo sixty. This gives a non-convex search space of integer vectors. The Genocop system is designed for convex search spaces, but we show how to adapt the Genocop operators to deal with this non-convex search space. The results of two experiments using the adapted operators are very encouraging. 1 The Rompnet The Rompnet is a railway system covering most of the real railway system in the Netherlands. The Rompnet case has been used as a test bed by the Dutch Railways, in their research on various scheduling techniques. First we introduce the Rompnet problem. The Rompnet is a railway system consisting of a number of railway stations and a number of railway sections, on which a number of trains are running. The departure times and halting times of all the trains in a railway system are xed by a timetable. So, a timetable is a schedule for a railway system. The quality of a timetable is determined by how good it meets certain requirements. There are a number of \hard constraints" imposed upon a timetable, which will be discussed below, but also a number of \soft constraints". Soft constraints can cause a considerable diierence in quality between two timetables which both satisfy all hard constraints. An example of a soft constraint might be minimizing the halting times of the trains in the railway system. In the Rompnet, every train runs every hour. Distinction is made between diierent types of trains and railway stations. Trains may have one of the following statuses: intercity train, interregion train, slow train, and are marked by the letters IC, IR and AR respectively. The status of a train determines the speed with which it travels, and at which railway stations it halts. Railway stations may have one of the following three statuses: IC: an intercity station; all trains halt here, IR: an interregion station; IR and AR trains halt here, AR: a slow train station; only AR trains halt here. The railway stations in the system are connected by railway sections. Of course, the net is not …